List questions from homotopy-theory

Published on 25 Mar 2026 - 12:52

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if two space are homotopy equivalent and one is connected, prove that the other is connected as well

Published on 15 Apr 2026 - 11:22

695

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Homotopy equivalence between finite, discrete topological spaces.

Published on 12 Apr 2026 - 0:13

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If $(X,A)$ has homotopy extension, then $X \times I$ def. retracts to $X \times \{0\} \cup A \times I$

Published on 15 Apr 2026 - 6:19

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what is the classifying space of a monoid

Published on 25 Mar 2026 - 19:10

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No retraction of $B^{n+1}$ onto $S^n$.

Published on 14 Apr 2026 - 10:26

490

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Ideas for basic application of homotopy theory to homological algebra?

Published on 12 Apr 2026 - 1:40

553

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canonical map of a monoid to its classifying space

Published on 25 Mar 2026 - 19:10

902

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Homotopy equivalence and chain complexes

Published on 06 May 2026 - 3:40

138

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what means 'the realization of a topological category'

Published on 16 Apr 2026 - 23:47

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Is $\mathbb{R}^n$ properly homotopy equivalent to $\mathbb{R}^m$ if $n \neq m$?

Published on 15 Apr 2026 - 2:39

73

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explicit equivalent relation in the expression of the classifying space of a monoid

Published on 25 Mar 2026 - 19:11

130

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Different groups with the same classifying space.

Published on 25 Mar 2026 - 19:17

124

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configuration space model for classifying space of monoid

Published on 25 Mar 2026 - 20:35

721

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The winding number (topological definition) is well-defined

Published on 12 Apr 2026 - 6:32

List Question

iterated loop spaces and configuration spaces

if two space are homotopy equivalent and one is connected, prove that the other is connected as well

Homotopy equivalence between finite, discrete topological spaces.

If $(X,A)$ has homotopy extension, then $X \times I$ def. retracts to $X \times \{0\} \cup A \times I$

what is the classifying space of a monoid

No retraction of $B^{n+1}$ onto $S^n$.

Ideas for basic application of homotopy theory to homological algebra?

canonical map of a monoid to its classifying space

Homotopy equivalence and chain complexes

what means 'the realization of a topological category'

Is $\mathbb{R}^n$ properly homotopy equivalent to $\mathbb{R}^m$ if $n \neq m$?

explicit equivalent relation in the expression of the classifying space of a monoid

Different groups with the same classifying space.

configuration space model for classifying space of monoid

The winding number (topological definition) is well-defined

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